PMC

Lattice models are generally the least complex, given the constraints to movement and interaction, whereas both CPM and lattice-free models possess varying degrees of complexity depending on the features included in the model. Miniature depictions of the respective images will be placed beside each subsection discussing morphogenetic ABMs in later sections to designate the types of models described. 2D, two-dimensional; 3D, three-dimensional; ABM, agent-based model; CPM, Cellular Potts Model.

A set of metrics is calculated or extracted from a series of pattern classes that depict typical cell organizations within the system—here, using the defined pattern classes from [, ]. The selected metrics should be equally represented in the simulated and experimental systems. Dimensional reduction techniques allow the multivariate data to be condensed to a few axes, ideally separating the defined pattern classes into distinct regions of the latent space. A transform function trained on the pattern class data can then be applied to metrics calculated from experimental and modeling results, mapping both into latent space and compared to the locations of the pattern classes. PCA, principal component analysis; t-SNE, t-distributed stochastic neighbor embedding.

(A) Cells are defined on a continuous 2D lattice such that a cell moving off the right edge of the grid reappears on the left edge. Divide and Die gradients are used to describe the behavior of different cell states in the crypt while movement up the crypt is the result of apoptosis. (B) A centroid model may be employed to investigate the role of crypt geometry on the location of anoikis within a crypt. The proliferative state of a cell is defined by prespecified regions along the crypt, and cell death is solely dependent on the occurrence of anoikis. (C) Centroid model that includes differentiation and dedifferentiation between the four main phenotypes present in an intestinal crypt. Wnt signaling is defined by the position within the crypt, whereas Notch signaling is determined by the phenotype of the cell and its neighbors. 2D, two-dimensional.

(A) Proliferation models depend on the differential division of cells, either between cell types with variable growth rates, between cell generations, or as an alternative to cell death. The illustration depicts volume exclusion of cell types A and B when cell type C has a fast division rate. (B) Migration models concentrate on directional movement, both in a purely migrational sense and in terms of polarized growth. The patterning of migration models is typically centered on overall morphology, such as the branched network of a vascular network. (C) The focus of differentiation models is on patterning that is reliant on fate change, in most cases following a hierarchy of lineage commitments. The interactions between the various cell types are major determinants for the resultant behavior.

(A) Archetypal Turing reaction–diffusion system with an activator and inhibitor generating repetitive patterns from differential diffusivities and nonlinear reaction terms. The reaction–diffusion system depends on the concept of a chemical prepattern developing in advance of cell fate decision and emphasizes the ability to induce pattern formation from an allegedly homogeneous initial state. (B) Wolpert’s positional information theory proposes an interpretation step based on concentration thresholds that alleviates the need for a morphogenetic pattern to match the chemical prepattern. In positional information, a cell is capable of multiple fate decisions from a single molecular gradient by discerning subtle variances in concentration along the gradient. (C) Agent-based modeling provides a framework capable of implementing features from both theories. Cell agents can act as the sources of activators (“A”) and inhibitors (“I”), permit localized reactions, and make autonomous decisions in response to their local environment. In addition to the generation of static patterns, agent-based modeling allows for the investigation of dynamic, spatiotemporal patterning.